A team wins 45% of its games. What is the probability the team will win all of its next three games?

Question

Any help with this statistics question? Thanks!

Answer 1

Hello Tara,

I will assume that the outcome (win or lose) of any game is independent of the outcome of any other game (or games). Let A = The event that the team wins the first of its next three games.

B = The team wins the second game.

C = The team wins the third game.

Saying that the team wins all of its next 3 games is the same as saying the team wins the first game, and the second, and the third. (Symbolically, A and B and C.) Thus, we want to find P(A and B and C). Because the events are independent,

P(A and B and C) = P(A)·P(B)·P(C)

Thus,

P(A and B and C) = (.45)(.45)(.45) = (.45)³

P(A and B and C) = .091125

Hope that helps! Let me know if you need any additional help.

William